The present invention relates to an optical-interference-type angular VELOCITY OR rate sensor wherein clockwise and counterclockwise light beams (hereinafter referred to as CW and CCW light beams) are passed through an optical path forming at least one loop and the phase difference between the CW and CCW light beams is detected to thereby measure an angular rate applied to the optical path about the axis thereof.
A description will be given, with reference to FIG. 1, of a conventional optical-interference-type angular rate sensor. It must be noted here that both the prior art and the present invention will be described in connection with a fiber optic gyro of the type employing an optical fiber as the above-mentioned optical path.
Light I from a light source 11 passes through an optical coupler 12, a polarizer 13 and an optical coupler 14 and then enters into an optical fiber coil 15 from its opposite ends. CW and CCW light beams which propagate through the optical fiber coil 15 are phase modulated by a phase modulator 16 disposed between one end of the optical fiber coil 15 and the optical coupler 14. The two phase-modulated light beams are combined by the optical coupler 14 into interference light, which is provided via the polarizer 13 to the optical coupler 12 and then branched therefrom to a photodetector 17 for photoelectric conversion.
With no angular rate .OMEGA. applied to the optical fiber coil 15 in its circumferential or peripheral direction, the phase difference between the two light beams in the optical fiber coil 15 is zero ideally, but the application of an angular rate causes a Sagnac phase difference .increment..PHI..sub.s which is expressed by the following equation: EQU .increment..PHI..sub.s =4.pi.RL ..PHI./C.lambda.
where C is the velocity of light, .lambda. is the wavelength of light in a vacuum, R is the radius of the optical fiber coil 15 and L is the length of the optical fiber of the optical fiber coil 15.
Based on a reference signal S.sub.r of a frequency f.sub.m from a reference signal generator 24, a phase modulation driver 22 generates a drive signal S.sub.p of the same frequency f.sub.m and applies it to the phase modulator 16. Letting the phase modulation of the CW and CCW light beams by the phase modulator 16 be represented by P(t)=Asin.omega..sub.m t,, the photoelectric conversion output Vp of the photodetector 17 can be expressed by the following equation: EQU V.sub.p =(I/2)K.sub.op K.sub.pd {1+cos.increment..PHI..sub.s [.SIGMA..epsilon..sub.n (-1).sup.n J.sub.2n (X)cos2n.omega..sub.m t']-sin.increment..PHI..sub.s [2.SIGMA.(-1).sup.n J.sub.2n+1 (X) co (2n+1).omega..sub.m t']} (2) X=2Asin.pi.f.sub.m .tau. (3)
.SIGMA.: summation operator from n=0 to infinity;
A: modulation index;
.omega..sub.m :angular frequency of phase modulation (.omega..sub.m =2.pi.f.sub.m);
.tau.: time for the propagation of light through the optical fiber coil 15;
t': t-.tau./2;
.epsilon..sub.n : 1 for n=0, .epsilon..sub.n =2 for n.gtoreq.1;
K.sub.op : optical loss on the emitted light I from the light source 11 which is caused or imposed by the optical path to the photodetector 17 via the optical fiber coil 15;
K.sub. pd: constant which is determined by a photoelectric conversion coefficient, an amplifier gain and so forth;
I: quantity of light emitted from the light source 11;
I.sub.o : maximum quantity of light which reaches the photodetector 17 (I.sub.o =K.sub.op.I);
J.sub.n : Bessel function of the first kind; and
.increment..PHI..sub.s : Sagnac phase difference between the CW and CCW light beams in the optical fiber coil 15.
The output Vp of the photodetector 17 is applied to a synchronous detector 18, wherein the same frequency component as the phase modulation frequency f.sub.m, that is, the fundamental harmonic component in Eq. (2), is synchronously detected by the reference signal S.sub.r of the same frequency from the reference signal generator 24. The detected output is applied to a low-pass filter 19, wherein its AC component is cut off, and the DC level corresponding to the fundamental harmonic component (i.e. the component of the frequency f.sub.m) in Eq. (2) is taken out with a proper gain, as the output of the fiber optic gyro (hereinafter referred to as an FOG output) at an output terminal 21.
The FOG output V.sub.1 is expressed by the following equation: ##EQU1## where K.sub.A1 is the total gain of the synchronous detector and the low-pass filter 19.
Hence the input angular rate .OMEGA. can be detected by measuring the output V.sub.1 of the low-pass filter 19.
A signal corresponding to the phase difference .increment..PHI..sub.s could be detected as the FOG output by the synchronous detection of an arbitrary one of the frequency components in Eq. (2), but it is customary in the art to detect the sin.increment..PHI..sub.s component (an odd harmonic component or simply called a sine component) which can be detected with the highest sensitivity when the phase difference .increment..PHI..sub.s is around zero. The detected output of such an arbitrary odd harmonic component can be expressed by changing the suffixed numerals in Eq. (4) to a value representing the selected odd harmonic.
The synchronously detected output V.sub.1 of the fiber optic gyro corresponding to the odd harmonic component (the fundamental harmonic component in this example) is a sine function using the phase difference .increment..PHI..sub.s as a variable, as is evident from Eq. (4) and, therefore, if the phase difference .increment..PHI..sub.s is sufficiently small, it can be regarded approximately to be equal to the sin.increment..PHI..sub.s component. Hence the FOG output V.sub.1 given by Eq. (4) exhibits an excellent linearity with respect to the phase difference .increment..PHI..sub.s, but an increase in the phase difference .increment..PHI..sub.s causes an increase in the linearity error. For example, when the phase difference .increment..PHI..sub.s is 45.degree., a 10% linearity error is induced .
Moreover, as is evident from Eq. (4), K.sub.1 is a proportional coefficient, and remains unchanged under stable circumferential conditions, but elements forming the coefficient K.sub.1 have some temperature coefficients and the input/output gain K.sub.1 of the fiber optic gyro, that is, its scale factor varies with temperature. For instance, the first-order Bessel function J.sub.1 (X) is relatively stable with respect to a temperature change of the phase modulation index A when the phase modulation index A is chosen such that X=1.84, and the constant K.sub.pd and the gain K.sub.A essentially have small temperature coefficients. However, there is a possibility that the optical loss K.sub.op varies about 30% when temperature changes in the range from -20.degree. C. to +70.degree. C.